The most relevant characteristics of an amplifier circuit are usually gain and bandwidth. In order to derive the bandwidth, an open loop response technique is used. The technique of looking at the open loop response provides information relating to the bandwidth and maximum achievable bandwidth of an amplifier circuit.
The DC gain of the open loop response is determined by opening the feedback loop and attaching a voltage source to an input side of the opened feedback loop. The output voltage is sensed at an output side of the opened feedback loop. To derive the bandwidth, the DC gain of the open loop response and the first dominant pole P1 are found. Assuming stable operation, there is only one dominant pole P1 located below the crossover frequency. The crossover frequency is the product of the DC gain of the open loop response and the first dominant pole P1. The crossover frequency usually defines the bandwidth of the closed-loop amplifier. The maximum available bandwidth is related to the second non-dominant pole P2.
Referring now to FIG. 1, an open loop response for an exemplary amplifier is shown. There is a constant gain from DC to a frequency of the first dominant pole P1. At the frequency of the pole P1, the gain begins falling. There is an inverse relationship between the gain and bandwidth of amplifiers. In general, higher gain values are associated with lower bandwidths, and lower gain values are associated with higher bandwidths.
Referring now to FIG. 2, it may be desirable to adjust the frequency of poles P1 and P2 for some applications. For example, it may be desirable for the amplifier to provide a relatively constant bandwidth at different gain values. In FIG. 2, the gain values are relatively constant from DC up to the frequency of the first dominant pole P1. Because the first dominant pole P1 is close to the second non-dominant pole P2, the gain values fall off sharply upon reaching the first dominant pole P1.
Various compensation techniques are known for adjusting the frequency of the poles of the amplifier. An operational amplifier (opamp) may be implemented using a two-stage amplifier. In two-stage amplifiers, Miller compensation or Ahuja compensation are sometimes used. Miller compensation employs a feedback capacitor connected across an input and output of the second amplifier stage. In Ahuja compensation, a current gain device is added in a feedback loop of the second amplifier stage.
Referring now to FIG. 3, it is sometimes difficult to adjust the frequencies of the poles P1 and P2 without creating stability problems. In FIG. 3, the phase response that is associated with the open loop response of FIG. 1 is shown. The phase response is 180 degrees from DC to about the frequency of the first pole P1. At the frequency of the pole P1, the phase response is approximately 90 degrees. The phase response remains at 90 degrees from the frequency of the first dominant pole P1 until about the frequency of the second non-dominant pole P2. At the frequency of the second non-dominant pole P2, the phase response is approximately zero degrees.
The phase response in FIG. 3 also illustrates a phase margin of approximately 90 degrees. The phase margin is usually defined at unity gain. For acceptable stability, the phase margin should be greater than approximately 55–60 degrees. Otherwise, oscillation will occur. Therefore, the 90 degree phase margin that is shown in FIG. 3 is typically acceptable. However, moving the frequency of the second non-dominant pole P2 closer to the zero crossing will reduce the phase margin. At some point, this will cause oscillation. Conversely, moving the first dominant pole P1 to a lower frequency in FIG. 1 will increase the phase margin. At some point, this too will cause oscillation. For these reasons, it is generally not possible to adjust the frequencies of the poles P1 and P2 shown in FIG. 1 to produce the open loop response of FIG. 2 without creating stability problems.
In one approach, Miller compensation is used to move a dominant pole of a gain stage to a lower frequency by increasing the effective input capacitance of the gain stage. Miller compensation circuits include a Miller capacitor that exploits the Miller effect. When the Miller capacitor is connected across an input and an output of an amplifier, the capacitance appears much larger from the input of the amplifier. While the dominant pole may be moved to a lower frequency using this approach, bandwidth of the system is still limited.
Referring now to FIG. 4, a Miller compensation circuit 10 includes first and second amplifiers 12 and 14, respectively. A capacitor 16 (or compensating capacitance) communicates with an input and an output of the second amplifier 14. An input voltage 18, Vin, of the Miller compensation circuit 10 is applied to an input of the first amplifier 12, and an output voltage 20, Vout, is referenced from the output of the second amplifier 14. The transconductance, gm1, of the first amplifier 12 may be increased to increase the overall bandwidth.
Without the addition of the capacitor 16, the circuit 10 is unstable by nature. This is because the nodes at the input and output of the second amplifier 14 are both high impedance nodes. The poles that exist at the two high impedance nodes are close in frequency, which creates instability in the circuit 10. The object of Miller compensation is to split the two poles. By adding the capacitor 16, one of the poles is pushed to a higher frequency and another is pushed to a lower frequency.
This ensures a single dominant pole system and a stable circuit 10. For example, a phase margin of approximately 90 degrees is achievable using Miller compensation. However, at high frequencies, the capacitor 16 functions as a short-circuit. When this happens, the input and output of the second amplifier 14 are shorted, and the combination of the capacitor 16 and the second amplifier 14 creates a diode-connected transistor. In this case, any noise from a reference potential is transferred to the output of the second amplifier 14. Additionally, the power supply rejection ratio (PSRR) of the circuit 10 is low during high frequency operation. Therefore, if a good PSRR is required, the circuit 10 is insufficient for desirable operation.
During low frequency operations, a feedback loop exists. The feedback loop functions to correct disturbances between nodes and the output of the circuit 10. However, during high frequency operations, the loop gain drops. Eventually, the loop gain diminishes, and the feedback loop is no longer able to correct disturbances at the output of the circuit 10. The result is a low PSRR at high frequencies.
Referring now to FIG. 5, an Ahuja compensation circuit 60 is created by adding a current gain device 62 in the feedback path. The current gain device 62 communicates with the first end of the capacitor 16, the output of the first amplifier 12, and the input of the second amplifier 14. A transconductance, gmc, is associated with the current gain device 62.
During high frequency operation, the capacitor 16 still functions as a short-circuit. However, noise from the reference potential no longer directly couples to the output of the circuit 60. This is because the second amplifier 14 no longer becomes a diode-connected transistor at high frequencies. This makes it possible for the circuit 60 to achieve a good PSRR at high frequencies.